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Title: | A strong completeness theorem for the gentzen systems associated with finite algebras |
Author: | Gil, Àngel J. Rebagliato, Jordi Verdú, B. (Buenaventura) |
Keywords: | Lògica matemàtica Teoria de la prova Universitat de Barcelona. Institut de Matemàtica |
Issue Date: | 1996 |
Publisher: | Universitat de Barcelona |
Series/Report no: | Mathematics Preprint Series; 218 |
Abstract: | In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems. |
Note: | Preprint enviat per a la seva publicació en una revista científica: Journal of Applied Non-Classical Logics. 1999, vol. 9, issue 1, pp 9-36. [http://doi.org/10.1080/11663081.1999.10510956] |
Note: | Reproducció digital del document original en paper [CRAI Biblioteca de Matemàtiques i Informàtica - Dipòsit Departament CAIXA 37.13] |
URI: | http://hdl.handle.net/2445/152101 |
Appears in Collections: | Preprints de Matemàtiques - Mathematics Preprint Series |
Files in This Item:
File | Description | Size | Format | |
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MPS_N218.pdf | 1.75 MB | Adobe PDF | View/Open |
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